Article 1, Section 8, Subsection 10- Congress is authorized to define and punish offenses against the laws of nations. Paul thought this was a fine clause to follow when he voted for the 'authorization to use force' in Afghanistan (after he said it was just for an oil pipeline, before he condemned it, then supported it, then condemned it again).. but ignored it when Iraq came up. He now plays semantic games over the word 'war' in subsection 11.. As Rush would say, all Symbolism over Substance.
That and the sections about letters of marque and reprisal are also operations less than all-out war. The Founders knew that there were situations that were best handled by strategies other than total war.
Congress' letter of authorization on Sep 18, 2001 constituted a letter from Congress to do whatever it took to destroy anyone or anything that had any part whatsoever, even peripherally, in the attack of 9/11.
Getting even, revenge, etc., are synonymns for "reprisal."
The Constitution Party is in the same boat. They would be appealing if they would recognize this same thing. The Constitution permits military action less than all-out war.
Also, there are reasons -- good ones -- for thinking this War on Terror should have been an all-out war. It should have been declared against Afghan, Iran, Iraq as the primary national sponsors of terror.